Axiom H: Horizon Saturation as an Identity — A Drafted Axiom, Its Two Addresses, and Its Price

This paper proposes an axiom. It does not derive the statement it proposes, it does not claim that any prior work derives it, and it presents no new derivation. After a nine-wave campaign in which every in-frame attempt to derive vacuum horizon saturation failed — sector by sector, functional by functional, formalism by formalism, count by count, map by map, and finally background by background — the saturation statement survives in exactly one honest form within the Aldred frame: as an axiom, adopted or declined, at a stated price. The axiom proposed here, Axiom H, states that the vacuum saturates its horizon as an identity; that the microstates counted by the vacuum's budget are the microstates of its boundary horizon; that the count is the horizon's Wald functional; and that for the cosmological horizon, S_vac = A/(4l_P^2) exactly. This paper states the axiom verbatim as it was drafted in Wave 7 of the campaign, exhibits its two equivalent addresses — posted on the region, in Wave 7's form, and posted at the seam, in the wall-form that Wave 9's junction ledger made available — prices it exactly as the sources price it, and states its falsifiability flanks exactly as they were stated when it was drafted. The axiom buys Lock 1, the saturation lock, closed by adoption; it gives the β_2 saturation postulate its one honest address; and it answers the equilibrium-collapse fence kinematically, by needing no dynamical route. It does not buy the residue 3Ω_Λ = 2.055: one measured point on the closed loop {Λ, V_4, B, S_dS} remains after adoption, exactly as before. It costs the whole conversion — the very identification the campaign was trying to derive is adopted instead of derived. The decision the axiom poses belongs to the author of the frame, and this paper records that decision as open and unmade.